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Multimodal exponential families of circular distributions with application to daily peak hours of PM2.5 level in a large city

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  • Sungsu Kim
  • Ashis SenGupta

Abstract

In this paper, we propose two multimodal circular distributions which are suitable for modeling circular data sets with two or more modes. Both distributions belong to the regular exponential family of distributions and are considered as extensions of the von Mises distribution. Hence, they possess the highly desirable properties, such as the existence of non-trivial sufficient statistics and optimal inferences for their parameters. Fine particulates (PM2.5) are generally emitted from activities such as industrial and residential combustion and from vehicle exhaust. We illustrate the utility of our proposed models using a real data set consisting of fine particulates (PM2.5) pollutant levels in Houston region during Fall season in 2019. Our results provide a strong evidence that its diurnal pattern exhibits four modes; two peaks during morning and evening rush hours and two peaks in between.

Suggested Citation

  • Sungsu Kim & Ashis SenGupta, 2021. "Multimodal exponential families of circular distributions with application to daily peak hours of PM2.5 level in a large city," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(16), pages 3193-3207, December.
    • Handle: RePEc:taf:japsta:v:48:y:2021:i:16:p:3193-3207
    DOI: 10.1080/02664763.2020.1796938
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